A new criterion for the normalized Haar measure to be a Pietsch measure

TL;DR

This paper introduces a new criterion to identify when the normalized Haar measure acts as a Pietsch measure for nonlinear summing mappings on compact topological groups, addressing an open problem.

Contribution

It provides a novel criterion that generalizes recent results and offers a partial solution to a problem posed by Botelho et al. and J. Diestel.

Findings

The criterion applies to a broad class of nonlinear summing mappings.

It encompasses both existing and new specific cases.

Partial resolution of an open problem in the field.

Abstract

In this paper we present a new criterion to determine when the normalized Haar measure on a compact topological group is a Pietsch measure for nonlinear summing mappings. As a consequence, we provide a partial answer to a problem raised by Botelho et al. in \cite{haar botelho} motivated by a question posed to the authors by J. Diestel. It is explicitly shown that this criterion encompasses recent and new results as particular cases.